What is 13.036363636... as a Fraction?

13.36 equals 71755 as a fraction.

How do you turn 13.36 repeating into a fraction?

Detailed Answer:

Step 1: To convert 13.36 repeating into a fraction, begin writing this simple equation:

n = 13.36 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (36), so multiply both sides by 10² = 100.

100 × n = 1336.36 (equation 2)

Step 3: Now subtract equation 1 from equation 2 to cancel the repeating block (or repetend) out.

100 × n = 1336.36
  1 × n = 13.36
 99 × n = 1323

132399 could be the answer, but it still can be put in the simplest form, i.e., reduced.

To simplify this fraction, divide the numerator and denominator by 9 (the GCF - greatest common factor).

n = 132399 = 1323 ÷ 999 ÷ 9 = 71755. So,

13.36 = 71755 as the lowest possible fraction.

As the numerator is greater than the denominator, we have an improper fraction, so we can also express it as a mixed number, thus 71755 is also equal to 13255 when expressed as a mixed number.

The repeating decimal 13.36 (vinculum notation) has a repeated block length of 2. It is also represented as 13.363636... (ellipsis notation) which equals approximately 13.3636363636 (decimal approximation)(*).

The recurring decimal 13.36 can be written as a ratio of two integers having 717 as the numerator and 55 as the denominator. So, it is a rational number (named after ratio). It can be shown that a number is rational if its decimal representation is repeating or terminating.

(*) At present, there is no single universally accepted notation or phrasing for repeating decimals.